| Proses pengerjaan |
- Pembayaran Pertama \({\rm{ = 2000v = 2000(1 + 7\% }}{{\rm{)}}^{{\rm{ – 1}}}} = 1869,158879\)
- 7 pembayaran berikutnya \({\rm{ = 2000}}\left( {\frac{{1,03}}{{{{1,07}^2}}} + \frac{{{{1,03}^2}}}{{{{1,07}^3}}} + … + \frac{{{{1,03}^7}}}{{{{1,07}^8}}}} \right)\)
\({\rm{ }}\left( {\frac{{1,03}}{{{{1,07}^2}}} + \frac{{{{1,03}^2}}}{{{{1,07}^3}}} + … + \frac{{{{1,03}^7}}}{{{{1,07}^8}}}} \right){\rm{ = }}{S_7} = \left( {\frac{{1,03}}{{1,07}}} \right)\left( {\frac{{1 – {{\left( {\frac{{1,03}}{{1,07}}} \right)}^7}}}{{1 – \left( {\frac{{1,03}}{{1,07}}} \right)}}} \right) = 5,63\)
\({\rm{ 2000}}\left( {\frac{{1,03}}{{{{1,07}^2}}} + \frac{{{{1,03}^2}}}{{{{1,07}^3}}} + … + \frac{{{{1,03}^7}}}{{{{1,07}^8}}}} \right) = {\rm{ 2000}}(5,63) = 11260\)
- \({\rm{2000(}}{1,03^7})\left( {\frac{{0,97}}{{{{1,07}^9}}} + \frac{{{{0,97}^2}}}{{{{1,07}^{10}}}} + … + \frac{{{{0,97}^8}}}{{{{1,07}^{16}}}}} \right)\)
\({\rm{ }}\left( {\frac{{0,97}}{{{{1,07}^9}}} + \frac{{{{0,97}^2}}}{{{{1,07}^{10}}}} + … + \frac{{{{0,97}^8}}}{{{{1,07}^{16}}}}} \right) = {S_8} = \left( {\frac{{0,97}}{{1,07}}} \right)\left( {\frac{{1 – {{\left( {\frac{{0,97}}{{1,07}}} \right)}^8}}}{{1 – \left( {\frac{{0,97}}{{1,07}}} \right)}}} \right) = 3,07\)
\({\rm{ 2000(}}{1,03^7})\left( {\frac{{0,97}}{{{{1,07}^9}}} + \frac{{{{0,97}^2}}}{{{{1,07}^{10}}}} + … + \frac{{{{0,97}^8}}}{{{{1,07}^{16}}}}} \right) = {\rm{2000(}}{1,03^7})(3,07) = 7552,219\)
\((i) + (ii) + (iii) = 20.688,63 \approx 20689\) |
